I actually didn't know that. I remember "Proffs and Refutations" being
optional reading for a course I took in mathematical logic, but (contrary to
my usual practice) I never got around to reading it. Sounds interesting.
On Tue, Dec 2, 2008 at 1:27 AM, Daniel Prager <danprager at optusnet.com.au>wrote:
>> On 02/12/2008, at 5:26 AM, Greg Woodhouse wrote:
>> A minor nit: There is no reason why mathematics cannot be taught as an
>> active process of discovery. The problem (well, one problem) is that the
>> only way to really learn mathematics is by doing, and that means
>> calculating. Still, there is no reason it can't be interesting. I'll give
>> you an example: one thing that always intrigued me, even as a child, is that
>> there are only 5 regular polyhedra (the tetrahedron, octahedron, cube,
>> dodecahedron and icosohedron), but I didn't realize until much later how
>> accessible a result it really is. You could almost make it a homework
>> exercise! Start with Euler's famous formula V - E + F = 2 (for a topological
>> sphere) and then suppose you have refgular polyhedron the faces of which are
>> n-gons. It all comes down to counting: If there are m of them, how many
>> times will you count each vertex in m times n vertices per face? How many
>> times will you count each edge? What happens if you plug these numbers in
>> Euler's formula? Even if youer students take euler's formula on faith, the
>> result is still impressive.
>>>>> An aside:
>> Greg's example of Euler's formula is used to good effect in a wonderful
> book by Lakatos, "Proofs and Refutations", that reads almost like a play
> about what an idealised mathematical classroom might look like. [If you
> "look inside" on Amazon, you can read the first few pages, which gives the
> flavor of the book.]
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